If the names on both passports are identical, this may suffice.
If there are discrepancies in names, birth dates, or other personal details, you may need to provide relevant documents that can establish the connection between the two identities.
Names are easy. But discrepancy over a birth date? Birthdates would have to be the same. Seen many times a spelling difference between a given name and birth certificate name where Jon is used but John was also used. Or when John became Jack.
I’ve seen differing dates of birth… some tin pot countries issue documents with arbitrary dates of birth. For instance everyone with 1st of a particular month.
Syria is a classic example of it (even before their war)…